LMFDB - Embedded newform 87.2.g.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			49.2
Root			$0.102196 - 0.128149i$ of defining polynomial
Character	$\chi$	$=$	87.49
Dual form			87.2.g.a.16.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04865 + 0.505001i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.402348 + 0.504528i) q^{4} +(-2.80239 + 1.34956i) q^{5} +(-1.04865 - 0.505001i) q^{6} +(1.08876 + 1.36527i) q^{7} +(0.685121 - 3.00171i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})$	\(q+(-1.04865 + 0.505001i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.402348 + 0.504528i) q^{4} +(-2.80239 + 1.34956i) q^{5} +(-1.04865 - 0.505001i) q^{6} +(1.08876 + 1.36527i) q^{7} +(0.685121 - 3.00171i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(2.25719 - 2.83042i) q^{10} +(0.616885 + 2.70275i) q^{11} -0.645316 q^{12} +(0.256556 + 1.12405i) q^{13} +(-1.83119 - 0.881853i) q^{14} +(-2.80239 - 1.34956i) q^{15} +(0.510226 + 2.23545i) q^{16} +2.64265 q^{17} +(-0.258994 - 1.13473i) q^{18} +(4.50431 - 5.64823i) q^{19} +(0.446645 - 1.95688i) q^{20} +(-0.388575 + 1.70246i) q^{21} +(-2.01179 - 2.52270i) q^{22} +(2.53201 + 1.21935i) q^{23} +(2.77400 - 1.33589i) q^{24} +(2.91464 - 3.65485i) q^{25} +(-0.836681 - 1.04917i) q^{26} +(-0.900969 + 0.433884i) q^{27} -1.12688 q^{28} +(-0.497296 - 5.36215i) q^{29} +3.62025 q^{30} +(-3.59066 + 1.72917i) q^{31} +(2.17538 + 2.72784i) q^{32} +(-1.72847 + 2.16744i) q^{33} +(-2.77121 + 1.33454i) q^{34} +(-4.89365 - 2.35666i) q^{35} +(-0.402348 - 0.504528i) q^{36} +(-2.32975 + 10.2073i) q^{37} +(-1.87107 + 8.19768i) q^{38} +(-0.718855 + 0.901415i) q^{39} +(2.13102 + 9.33659i) q^{40} +8.92649 q^{41} +(-0.452266 - 1.98151i) q^{42} +(-10.6279 - 5.11815i) q^{43} +(-1.61181 - 0.776209i) q^{44} +(-0.692134 - 3.03244i) q^{45} -3.27095 q^{46} +(1.63447 + 7.16106i) q^{47} +(-1.42962 + 1.79269i) q^{48} +(0.879102 - 3.85160i) q^{49} +(-1.21073 + 5.30454i) q^{50} +(1.64767 + 2.06611i) q^{51} +(-0.670338 - 0.322818i) q^{52} +(4.85314 - 2.33715i) q^{53} +(0.725685 - 0.909981i) q^{54} +(-5.37628 - 6.74164i) q^{55} +(4.84407 - 2.33278i) q^{56} +7.22436 q^{57} +(3.22938 + 5.37187i) q^{58} -8.20042 q^{59} +(1.80843 - 0.870893i) q^{60} +(3.06034 + 3.83755i) q^{61} +(2.89209 - 3.62657i) q^{62} +(-1.57331 + 0.757665i) q^{63} +(-7.79050 - 3.75171i) q^{64} +(-2.23594 - 2.80378i) q^{65} +(0.717998 - 3.14575i) q^{66} +(0.100933 - 0.442217i) q^{67} +(-1.06326 + 1.33329i) q^{68} +(0.625354 + 2.73985i) q^{69} +6.32182 q^{70} +(-2.58226 - 11.3136i) q^{71} +(2.77400 + 1.33589i) q^{72} +(11.5822 + 5.57770i) q^{73} +(-2.71162 - 11.8804i) q^{74} +4.67473 q^{75} +(1.03739 + 4.54510i) q^{76} +(-3.01833 + 3.78486i) q^{77} +(0.298608 - 1.30829i) q^{78} +(3.43076 - 15.0312i) q^{79} +(-4.44673 - 5.57602i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(-9.36072 + 4.50789i) q^{82} +(-2.62789 + 3.29527i) q^{83} +(-0.702595 - 0.881027i) q^{84} +(-7.40575 + 3.56642i) q^{85} +13.7296 q^{86} +(3.88224 - 3.73205i) q^{87} +8.53551 q^{88} +(1.83072 - 0.881630i) q^{89} +(2.25719 + 2.83042i) q^{90} +(-1.25529 + 1.57409i) q^{91} +(-1.63394 + 0.786865i) q^{92} +(-3.59066 - 1.72917i) q^{93} +(-5.33032 - 6.68401i) q^{94} +(-5.00022 + 21.9074i) q^{95} +(-0.776385 + 3.40157i) q^{96} +(7.89711 - 9.90266i) q^{97} +(1.02319 + 4.48291i) q^{98} -2.77225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.04865	+	0.505001i	−0.741505	+	0.357090i	−0.766197	−	0.642605i	$-0.777854\pi$
$2$	−1.04865	+	0.505001i	−0.741505	+	0.357090i	0.0246928	+	0.999695i	$0.492139\pi$
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$3$	0.623490	+	0.781831i	0.359972	+	0.451391i
$4$	−0.402348	+	0.504528i	−0.201174	+	0.252264i
$5$	−2.80239	+	1.34956i	−1.25327	+	0.603542i	−0.938386	−	0.345588i	$-0.887679\pi$
$5$	−2.80239	+	1.34956i	−1.25327	+	0.603542i	−0.314882	+	0.949131i	$0.601965\pi$
$6$	−1.04865	−	0.505001i	−0.428108	−	0.206166i
$7$	1.08876	+	1.36527i	0.411514	+	0.516022i	0.943789	−	0.330550i	$-0.107234\pi$
$7$	1.08876	+	1.36527i	0.411514	+	0.516022i	−0.532275	+	0.846572i	$0.678663\pi$
$8$	0.685121	−	3.00171i	0.242227	−	1.06127i
$9$	−0.222521	+	0.974928i	−0.0741736	+	0.324976i
$10$	2.25719	−	2.83042i	0.713786	−	0.895059i
$11$	0.616885	+	2.70275i	0.185998	+	0.814909i	0.978699	+	0.205299i	$0.0658168\pi$
$11$	0.616885	+	2.70275i	0.185998	+	0.814909i	−0.792701	+	0.609610i	$0.791326\pi$
$12$	−0.645316			−0.186287
$13$	0.256556	+	1.12405i	0.0711559	+	0.311754i	0.997964	−	0.0637811i	$-0.0203160\pi$
$13$	0.256556	+	1.12405i	0.0711559	+	0.311754i	−0.926808	+	0.375535i	$0.877459\pi$
$14$	−1.83119	−	0.881853i	−0.489405	−	0.235685i
$15$	−2.80239	−	1.34956i	−0.723575	−	0.348455i
$16$	0.510226	+	2.23545i	0.127557	+	0.558862i
$17$	2.64265			0.640937			0.320469	−	0.947259i	$-0.396160\pi$
$17$	2.64265			0.640937			0.320469	+	0.947259i	$0.396160\pi$
$18$	−0.258994	−	1.13473i	−0.0610455	−	0.267458i
$19$	4.50431	−	5.64823i	1.03336	−	1.29579i	0.0790836	−	0.996868i	$-0.474801\pi$
$19$	4.50431	−	5.64823i	1.03336	−	1.29579i	0.954277	−	0.298925i	$-0.0966280\pi$
$20$	0.446645	−	1.95688i	0.0998728	−	0.437571i
$21$	−0.388575	+	1.70246i	−0.0847940	+	0.371507i
$22$	−2.01179	−	2.52270i	−0.428914	−	0.537841i
$23$	2.53201	+	1.21935i	0.527960	+	0.254252i	0.678822	−	0.734303i	$-0.262491\pi$
$23$	2.53201	+	1.21935i	0.527960	+	0.254252i	−0.150862	+	0.988555i	$0.548205\pi$
$24$	2.77400	−	1.33589i	0.566240	−	0.272687i
$25$	2.91464	−	3.65485i	0.582929	−	0.730970i
$26$	−0.836681	−	1.04917i	−0.164087	−	0.205758i
$27$	−0.900969	+	0.433884i	−0.173392	+	0.0835010i
$28$	−1.12688			−0.212959
$29$	−0.497296	−	5.36215i	−0.0923456	−	0.995727i
$29$	−0.497296	−	5.36215i	−0.0923456	−	0.995727i
$30$	3.62025			0.660964
$31$	−3.59066	+	1.72917i	−0.644901	+	0.310568i	−0.727595	−	0.686007i	$-0.759362\pi$
$31$	−3.59066	+	1.72917i	−0.644901	+	0.310568i	0.0826940	+	0.996575i	$0.473648\pi$
$32$	2.17538	+	2.72784i	0.384557	+	0.482219i
$33$	−1.72847	+	2.16744i	−0.300888	+	0.377302i
$34$	−2.77121	+	1.33454i	−0.475258	+	0.228872i
$35$	−4.89365	−	2.35666i	−0.827178	−	0.398348i
$36$	−0.402348	−	0.504528i	−0.0670579	−	0.0840880i
$37$	−2.32975	+	10.2073i	−0.383009	+	1.67807i	0.304988	+	0.952356i	$0.401348\pi$
$37$	−2.32975	+	10.2073i	−0.383009	+	1.67807i	−0.687996	+	0.725714i	$0.741509\pi$
$38$	−1.87107	+	8.19768i	−0.303527	+	1.32984i
$39$	−0.718855	+	0.901415i	−0.115109	+	0.144342i
$40$	2.13102	+	9.33659i	0.336943	+	1.47624i
$41$	8.92649			1.39408			0.697041	−	0.717031i	$-0.254499\pi$
$41$	8.92649			1.39408			0.697041	+	0.717031i	$0.254499\pi$
$42$	−0.452266	−	1.98151i	−0.0697861	−	0.305753i
$43$	−10.6279	−	5.11815i	−1.62075	−	0.780510i	−0.620752	−	0.784007i	$-0.713173\pi$
$43$	−10.6279	−	5.11815i	−1.62075	−	0.780510i	−0.999994	+	0.00349639i	$0.998887\pi$
$44$	−1.61181	−	0.776209i	−0.242990	−	0.117018i
$45$	−0.692134	−	3.03244i	−0.103177	−	0.452049i
$46$	−3.27095			−0.482275
$47$	1.63447	+	7.16106i	0.238411	+	1.04455i	0.942440	+	0.334376i	$0.108526\pi$
$47$	1.63447	+	7.16106i	0.238411	+	1.04455i	−0.704028	+	0.710172i	$0.748617\pi$
$48$	−1.42962	+	1.79269i	−0.206348	+	0.258753i
$49$	0.879102	−	3.85160i	0.125586	−	0.550228i
$50$	−1.21073	+	5.30454i	−0.171223	+	0.750175i
$51$	1.64767	+	2.06611i	0.230720	+	0.289313i
$52$	−0.670338	−	0.322818i	−0.0929591	−	0.0447667i
$53$	4.85314	−	2.33715i	0.666629	−	0.321032i	−0.0697855	−	0.997562i	$-0.522231\pi$
$53$	4.85314	−	2.33715i	0.666629	−	0.321032i	0.736415	+	0.676530i	$0.236517\pi$
$54$	0.725685	−	0.909981i	0.0987533	−	0.123833i
$55$	−5.37628	−	6.74164i	−0.724937	−	0.909043i
$56$	4.84407	−	2.33278i	0.647316	−	0.311731i
$57$	7.22436			0.956889
$58$	3.22938	+	5.37187i	0.424039	+	0.705361i
$59$	−8.20042			−1.06760			−0.533802	−	0.845610i	$-0.679237\pi$
$59$	−8.20042			−1.06760			−0.533802	+	0.845610i	$0.679237\pi$
$60$	1.80843	−	0.870893i	0.233467	−	0.112432i
$61$	3.06034	+	3.83755i	0.391837	+	0.491348i	0.938148	−	0.346234i	$-0.112540\pi$
$61$	3.06034	+	3.83755i	0.391837	+	0.491348i	−0.546311	+	0.837582i	$0.683968\pi$
$62$	2.89209	−	3.62657i	0.367296	−	0.460575i
$63$	−1.57331	+	0.757665i	−0.198218	+	0.0954568i
$64$	−7.79050	−	3.75171i	−0.973813	−	0.468963i
$65$	−2.23594	−	2.80378i	−0.277334	−	0.347766i
$66$	0.717998	−	3.14575i	0.0883794	−	0.387216i
$67$	0.100933	−	0.442217i	0.0123309	−	0.0540254i	−0.968388	−	0.249448i	$-0.919751\pi$
$67$	0.100933	−	0.442217i	0.0123309	−	0.0540254i	0.980719	+	0.195423i	$0.0626079\pi$
$68$	−1.06326	+	1.33329i	−0.128940	+	0.161685i
$69$	0.625354	+	2.73985i	0.0752837	+	0.329840i
$70$	6.32182			0.755602
$71$	−2.58226	−	11.3136i	−0.306458	−	1.34268i	−0.860185	−	0.509983i	$-0.829652\pi$
$71$	−2.58226	−	11.3136i	−0.306458	−	1.34268i	0.553726	−	0.832699i	$-0.313205\pi$
$72$	2.77400	+	1.33589i	0.326919	+	0.157436i
$73$	11.5822	+	5.57770i	1.35559	+	0.652820i	0.963650	−	0.267169i	$-0.0860880\pi$
$73$	11.5822	+	5.57770i	1.35559	+	0.652820i	0.391945	+	0.919989i	$0.371802\pi$
$74$	−2.71162	−	11.8804i	−0.315219	−	1.38107i
$75$	4.67473			0.539791
$76$	1.03739	+	4.54510i	0.118997	+	0.521359i
$77$	−3.01833	+	3.78486i	−0.343970	+	0.431325i
$78$	0.298608	−	1.30829i	0.0338107	−	0.148134i
$79$	3.43076	−	15.0312i	0.385991	−	1.69114i	−0.292286	−	0.956331i	$-0.594416\pi$
$79$	3.43076	−	15.0312i	0.385991	−	1.69114i	0.678277	−	0.734807i	$-0.262727\pi$
$80$	−4.44673	−	5.57602i	−0.497160	−	0.623418i
$81$	−0.900969	−	0.433884i	−0.100108	−	0.0482093i
$82$	−9.36072	+	4.50789i	−1.03372	+	0.497813i
$83$	−2.62789	+	3.29527i	−0.288448	+	0.361702i	−0.904851	−	0.425728i	$-0.860018\pi$
$83$	−2.62789	+	3.29527i	−0.288448	+	0.361702i	0.616403	+	0.787431i	$0.288589\pi$
$84$	−0.702595	−	0.881027i	−0.0766594	−	0.0961279i
$85$	−7.40575	+	3.56642i	−0.803267	+	0.386833i
$86$	13.7296			1.48050
$87$	3.88224	−	3.73205i	0.416220	−	0.400118i
$88$	8.53551			0.909889
$89$	1.83072	−	0.881630i	0.194056	−	0.0934526i	−0.334332	−	0.942455i	$-0.608511\pi$
$89$	1.83072	−	0.881630i	0.194056	−	0.0934526i	0.528389	+	0.849003i	$0.322796\pi$
$90$	2.25719	+	2.83042i	0.237929	+	0.298353i
$91$	−1.25529	+	1.57409i	−0.131590	+	0.165009i
$92$	−1.63394	+	0.786865i	−0.170350	+	0.0820364i
$93$	−3.59066	−	1.72917i	−0.372334	−	0.179306i
$94$	−5.33032	−	6.68401i	−0.549780	−	0.689403i
$95$	−5.00022	+	21.9074i	−0.513012	+	2.24765i
$96$	−0.776385	+	3.40157i	−0.0792395	+	0.347171i
$97$	7.89711	−	9.90266i	0.801830	−	1.00546i	−0.197852	−	0.980232i	$-0.563396\pi$
$97$	7.89711	−	9.90266i	0.801830	−	1.00546i	0.999682	−	0.0252311i	$-0.00803215\pi$
$98$	1.02319	+	4.48291i	0.103358	+	0.452842i
$99$	−2.77225			−0.278622
$100$	0.671273	+	2.94104i	0.0671273	+	0.294104i
$101$	−2.85191	−	1.37341i	−0.283776	−	0.136659i	0.286582	−	0.958056i	$-0.407481\pi$
$101$	−2.85191	−	1.37341i	−0.283776	−	0.136659i	−0.570358	+	0.821397i	$0.693195\pi$
$102$	−2.77121	−	1.33454i	−0.274390	−	0.132139i
$103$	−0.582986	−	2.55423i	−0.0574433	−	0.251676i	0.938051	−	0.346497i	$-0.112629\pi$
$103$	−0.582986	−	2.55423i	−0.0574433	−	0.251676i	−0.995494	+	0.0948218i	$0.969772\pi$
$104$	3.54984			0.348090
$105$	−1.20863	−	5.29536i	−0.117950	−	0.516774i
$106$	−3.90896	+	4.90168i	−0.379672	+	0.476093i
$107$	2.23430	−	9.78910i	0.215998	−	0.946348i	−0.744404	−	0.667730i	$-0.767266\pi$
$107$	2.23430	−	9.78910i	0.215998	−	0.946348i	0.960402	−	0.278619i	$-0.0898766\pi$
$108$	0.143596	−	0.629136i	0.0138176	−	0.0605387i
$109$	−2.87905	−	3.61022i	−0.275763	−	0.345796i	0.624593	−	0.780951i	$-0.285265\pi$
$109$	−2.87905	−	3.61022i	−0.275763	−	0.345796i	−0.900356	+	0.435155i	$0.856694\pi$
$110$	9.04235	+	4.35457i	0.862154	+	0.415192i
$111$	−9.43297	+	4.54268i	−0.895338	+	0.431172i
$112$	−2.49646	+	3.13047i	−0.235894	+	0.295801i
$113$	−3.23577	−	4.05752i	−0.304395	−	0.381700i	0.605982	−	0.795478i	$-0.292780\pi$
$113$	−3.23577	−	4.05752i	−0.304395	−	0.381700i	−0.910378	+	0.413779i	$0.864209\pi$
$114$	−7.57579	+	3.64831i	−0.709538	+	0.341695i
$115$	−8.74126			−0.815127
$116$	2.90544	+	1.90655i	0.269764	+	0.177019i
$117$	−1.15295			−0.106591
$118$	8.59933	−	4.14122i	0.791633	−	0.381230i
$119$	2.87722	+	3.60792i	0.263754	+	0.330738i
$120$	−5.97098	+	7.48737i	−0.545073	+	0.683500i
$121$	2.98635	−	1.43815i	0.271487	−	0.130741i
$122$	−5.14719	−	2.47875i	−0.466004	−	0.224416i
$123$	5.56557	+	6.97901i	0.501831	+	0.629276i
$124$	0.572278	−	2.50731i	0.0513921	−	0.225163i
$125$	0.225132	−	0.986369i	0.0201364	−	0.0882235i
$126$	1.26722	−	1.58904i	0.112893	−	0.141563i
$127$	3.34102	+	14.6380i	0.296467	+	1.29891i	0.875347	+	0.483496i	$0.160633\pi$
$127$	3.34102	+	14.6380i	0.296467	+	1.29891i	−0.578879	+	0.815413i	$0.696510\pi$
$128$	3.08601			0.272767
$129$	−2.62489	−	11.5004i	−0.231108	−	1.01255i
$130$	3.76062	+	1.81102i	0.329829	+	0.158837i
$131$	0.482335	+	0.232280i	0.0421418	+	0.0202944i	0.454836	−	0.890575i	$-0.349698\pi$
$131$	0.482335	+	0.232280i	0.0421418	+	0.0202944i	−0.412694	+	0.910870i	$0.635412\pi$
$132$	−0.398085	−	1.74413i	−0.0346489	−	0.151807i
$133$	12.6155			1.09390
$134$	0.117477	+	0.514700i	0.0101485	+	0.0444633i
$135$	1.93932	−	2.43183i	0.166910	−	0.209298i
$136$	1.81054	−	7.93248i	0.155252	−	0.680205i
$137$	−2.77503	+	12.1582i	−0.237087	+	1.03874i	0.706525	+	0.707688i	$0.250262\pi$
$137$	−2.77503	+	12.1582i	−0.237087	+	1.03874i	−0.943611	+	0.331056i	$0.892595\pi$
$138$	−2.03940	−	2.55733i	−0.173606	−	0.217695i
$139$	7.82790	+	3.76972i	0.663954	+	0.319743i	0.735333	−	0.677706i	$-0.237026\pi$
$139$	7.82790	+	3.76972i	0.663954	+	0.319743i	−0.0713790	+	0.997449i	$0.522740\pi$
$140$	3.15795	−	1.52079i	0.266895	−	0.128530i
$141$	−4.57967	+	5.74272i	−0.385678	+	0.483625i
$142$	8.42128	+	10.5600i	0.706698	+	0.886172i
$143$	−2.87975	+	1.38681i	−0.240817	+	0.115971i
$144$	−2.29294			−0.191078
$145$	8.63018	+	14.3557i	0.716697	+	1.19218i
$146$	−14.9624			−1.23830
$147$	3.55941	−	1.71412i	0.293575	−	0.141378i
$148$	−4.21250	−	5.28231i	−0.346265	−	0.434203i
$149$	−9.37128	+	11.7512i	−0.767726	+	0.962697i	−0.999950	−	0.00996473i	$-0.996828\pi$
$149$	−9.37128	+	11.7512i	−0.767726	+	0.962697i	0.232225	+	0.972662i	$0.425400\pi$
$150$	−4.90213	+	2.36074i	−0.400258	+	0.192754i
$151$	−13.5900	−	6.54459i	−1.10594	−	0.532591i	−0.210417	−	0.977612i	$-0.567482\pi$
$151$	−13.5900	−	6.54459i	−1.10594	−	0.532591i	−0.895521	+	0.445020i	$0.853196\pi$
$152$	−13.8684	−	17.3904i	−1.12487	−	1.41055i
$153$	−0.588045	+	2.57640i	−0.0475407	+	0.208289i
$154$	1.25380	−	5.49324i	0.101034	−	0.442658i
$155$	7.72881	−	9.69162i	0.620793	−	0.778450i
$156$	−0.165560	−	0.725364i	−0.0132554	−	0.0580756i
$157$	−9.94273			−0.793517			−0.396758	−	0.917923i	$-0.629865\pi$
$157$	−9.94273			−0.793517			−0.396758	+	0.917923i	$0.629865\pi$
$158$	3.99310	+	17.4949i	0.317674	+	1.39182i
$159$	4.85314	+	2.33715i	0.384879	+	0.185348i
$160$	−9.77767	−	4.70868i	−0.772993	−	0.372254i
$161$	1.09202	+	4.78444i	0.0860630	+	0.377067i
$162$	1.16391			0.0914453
$163$	0.610696	+	2.67563i	0.0478334	+	0.209572i	0.993197	−	0.116446i	$-0.0371502\pi$
$163$	0.610696	+	2.67563i	0.0478334	+	0.209572i	−0.945364	+	0.326018i	$0.894293\pi$
$164$	−3.59155	+	4.50366i	−0.280453	+	0.351677i
$165$	1.91877	−	8.40669i	0.149376	−	0.654460i
$166$	1.09161	−	4.78265i	0.0847253	−	0.371206i
$167$	−1.98862	−	2.49365i	−0.153884	−	0.192964i	0.698914	−	0.715206i	$-0.253667\pi$
$167$	−1.98862	−	2.49365i	−0.153884	−	0.192964i	−0.852797	+	0.522242i	$0.825096\pi$
$168$	4.84407	+	2.33278i	0.373728	+	0.179978i
$169$	10.5149	−	5.06373i	0.808841	−	0.389517i
$170$	5.96496	−	7.47983i	0.457492	−	0.573677i
$171$	4.50431	+	5.64823i	0.344453	+	0.431931i
$172$	6.85838	−	3.30282i	0.522946	−	0.251838i
$173$	7.57784			0.576132			0.288066	−	0.957611i	$-0.406988\pi$
$173$	7.57784			0.576132			0.288066	+	0.957611i	$0.406988\pi$
$174$	−2.18641	+	5.87414i	−0.165751	+	0.445317i
$175$	8.16319			0.617079
$176$	−5.72710	+	2.75803i	−0.431697	+	0.207894i
$177$	−5.11288	−	6.41134i	−0.384307	−	0.481906i
$178$	−1.47456	+	1.84904i	−0.110523	+	0.138591i
$179$	2.53345	−	1.22005i	0.189359	−	0.0911906i	−0.336802	−	0.941576i	$-0.609345\pi$
$179$	2.53345	−	1.22005i	0.189359	−	0.0911906i	0.526161	+	0.850385i	$0.323631\pi$
$180$	1.80843	+	0.870893i	0.134792	+	0.0649125i
$181$	4.38980	+	5.50464i	0.326292	+	0.409157i	0.917737	−	0.397188i	$-0.130014\pi$
$181$	4.38980	+	5.50464i	0.326292	+	0.409157i	−0.591446	+	0.806345i	$0.701443\pi$
$182$	0.521441	−	2.28458i	0.0386518	−	0.169345i
$183$	−1.09222	+	4.78535i	−0.0807395	+	0.353743i
$184$	5.39487	−	6.76495i	0.397715	−	0.498719i
$185$	−7.24651	−	31.7490i	−0.532774	−	2.33424i
$186$	4.63856			0.340116
$187$	1.63021	+	7.14243i	0.119213	+	0.522306i
$188$	−4.27058	−	2.05660i	−0.311464	−	0.149993i
$189$	−1.57331	−	0.757665i	−0.114441	−	0.0551120i
$190$	−5.81981	−	25.4982i	−0.422213	−	1.84984i
$191$	4.42589			0.320246			0.160123	−	0.987097i	$-0.448811\pi$
$191$	4.42589			0.320246			0.160123	+	0.987097i	$0.448811\pi$
$192$	−1.92409	−	8.43001i	−0.138860	−	0.608384i
$193$	−2.51833	+	3.15788i	−0.181273	+	0.227309i	−0.864163	−	0.503212i	$-0.832151\pi$
$193$	−2.51833	+	3.15788i	−0.181273	+	0.227309i	0.682890	+	0.730521i	$0.260723\pi$
$194$	−3.28041	+	14.3724i	−0.235520	+	1.03188i
$195$	0.797998	−	3.49626i	0.0571458	−	0.250372i
$196$	1.58953	+	1.99321i	0.113538	+	0.142372i
$197$	−10.8033	−	5.20261i	−0.769706	−	0.370671i	0.00745564	−	0.999972i	$-0.497627\pi$
$197$	−10.8033	−	5.20261i	−0.769706	−	0.370671i	−0.777161	+	0.629302i	$0.783341\pi$
$198$	2.90711	−	1.39999i	0.206600	−	0.0994931i
$199$	0.858565	−	1.07661i	0.0608621	−	0.0763187i	−0.750469	−	0.660906i	$-0.770172\pi$
$199$	0.858565	−	1.07661i	0.0608621	−	0.0763187i	0.811331	+	0.584587i	$0.198744\pi$
$200$	−8.97392	−	11.2529i	−0.634552	−	0.795703i
$201$	0.408670	−	0.196805i	0.0288253	−	0.0138815i
$202$	3.68422			0.259221
$203$	6.77932	−	6.51705i	0.475815	−	0.457408i
$204$	−1.70534			−0.119398
$205$	−25.0155	+	12.0468i	−1.74716	+	0.841388i
$206$	1.90123	+	2.38407i	0.132465	+	0.166106i
$207$	−1.75220	+	2.19719i	−0.121786	+	0.152715i
$208$	−2.38185	+	1.14704i	−0.165151	+	0.0795327i
$209$	18.0444	+	8.68972i	1.24816	+	0.601080i
$210$	3.94159	+	4.94260i	0.271996	+	0.341072i
$211$	3.86605	−	16.9383i	0.266150	−	1.16608i	−0.648301	−	0.761384i	$-0.724520\pi$
$211$	3.86605	−	16.9383i	0.266150	−	1.16608i	0.914451	−	0.404696i	$-0.132623\pi$
$212$	−0.773492	+	3.38889i	−0.0531236	+	0.232750i
$213$	7.23534	−	9.07283i	0.495758	−	0.621660i
$214$	2.60052	+	11.3936i	0.177768	+	0.778852i
$215$	36.6909			2.50230
$216$	0.685121	+	3.00171i	0.0466166	+	0.204241i
$217$	−6.27014	−	3.01954i	−0.425645	−	0.204980i
$218$	4.84227	+	2.33191i	0.327960	+	0.157937i
$219$	2.86057	+	12.5330i	0.193299	+	0.846900i
$220$	5.56448			0.375157
$221$	0.677989	+	2.97046i	0.0456065	+	0.199815i
$222$	7.59779	−	9.52732i	0.509930	−	0.639432i
$223$	−3.08597	+	13.5205i	−0.206652	+	0.905402i	0.760124	+	0.649778i	$0.225138\pi$
$223$	−3.08597	+	13.5205i	−0.206652	+	0.905402i	−0.966776	+	0.255624i	$0.917719\pi$
$224$	−1.35575	+	5.93995i	−0.0905852	+	0.396880i
$225$	2.91464	+	3.65485i	0.194310	+	0.243657i
$226$	5.44223	+	2.62084i	0.362012	+	0.174336i
$227$	−2.15378	+	1.03721i	−0.142952	+	0.0688419i	−0.503992	−	0.863708i	$-0.668136\pi$
$227$	−2.15378	+	1.03721i	−0.142952	+	0.0688419i	0.361040	+	0.932550i	$0.382422\pi$
$228$	−2.90670	+	3.64489i	−0.192501	+	0.241389i
$229$	0.665955	+	0.835081i	0.0440075	+	0.0551837i	0.803348	−	0.595510i	$-0.203050\pi$
$229$	0.665955	+	0.835081i	0.0440075	+	0.0551837i	−0.759341	+	0.650693i	$0.774478\pi$
$230$	9.16649	−	4.41435i	0.604420	−	0.291074i
$231$	−4.84102			−0.318516
$232$	−16.4364	−	2.18098i	−1.07910	−	0.143189i
$233$	−25.6684			−1.68159			−0.840795	−	0.541353i	$-0.817912\pi$
$233$	−25.6684			−1.68159			−0.840795	+	0.541353i	$0.817912\pi$
$234$	1.20904	−	0.582243i	0.0790374	−	0.0380624i
$235$	−14.2447	−	17.8623i	−0.929222	−	1.16521i
$236$	3.29942	−	4.13734i	0.214774	−	0.269318i
$237$	13.8909	−	6.68950i	0.902310	−	0.434529i
$238$	−4.83919	−	2.33043i	−0.313678	−	0.151059i
$239$	−4.90036	−	6.14486i	−0.316978	−	0.397478i	0.597661	−	0.801749i	$-0.296097\pi$
$239$	−4.90036	−	6.14486i	−0.316978	−	0.397478i	−0.914639	+	0.404271i	$0.867525\pi$
$240$	1.58702	−	6.95319i	0.102442	−	0.448826i
$241$	−5.44182	+	23.8422i	−0.350539	+	1.53581i	0.425402	+	0.905005i	$0.360133\pi$
$241$	−5.44182	+	23.8422i	−0.350539	+	1.53581i	−0.775941	+	0.630806i	$0.782724\pi$
$242$	−2.40536	+	3.01623i	−0.154622	+	0.193890i
$243$	−0.222521	−	0.974928i	−0.0142747	−	0.0625417i
$244$	−3.16747			−0.202777
$245$	2.73438	+	11.9801i	0.174693	+	0.765380i
$246$	−9.36072	−	4.50789i	−0.596818	−	0.287412i
$247$	7.50448	+	3.61397i	0.477499	+	0.229951i
$248$	2.73043	+	11.9628i	0.173383	+	0.759639i
$249$	−4.21480			−0.267102
$250$	0.262034	+	1.14804i	0.0165725	+	0.0726087i
$251$	−3.72725	+	4.67383i	−0.235262	+	0.295009i	−0.885422	−	0.464788i	$-0.846130\pi$
$251$	−3.72725	+	4.67383i	−0.235262	+	0.295009i	0.650160	+	0.759797i	$0.274702\pi$
$252$	0.250753	−	1.09862i	0.0157960	−	0.0692067i
$253$	−1.73364	+	7.59557i	−0.108993	+	0.477529i
$254$	−10.8957	−	13.6628i	−0.683659	−	0.857281i
$255$	−7.40575	−	3.56642i	−0.463766	−	0.223338i
$256$	12.3449	−	5.94498i	0.771555	−	0.371561i
$257$	16.7993	−	21.0657i	1.04791	−	1.31404i	0.100183	−	0.994969i	$-0.468057\pi$
$257$	16.7993	−	21.0657i	1.04791	−	1.31404i	0.947730	−	0.319073i	$-0.103371\pi$
$258$	8.56028	+	10.7343i	0.532940	+	0.668285i
$259$	−16.4722	+	7.93260i	−1.02353	+	0.492908i
$260$	2.31421			0.143521
$261$	5.33837	+	0.708363i	0.330437	+	0.0438466i
$262$	−0.623100			−0.0384952
$263$	−14.9862	+	7.21695i	−0.924086	+	0.445016i	−0.834528	−	0.550965i	$-0.814260\pi$
$263$	−14.9862	+	7.21695i	−0.924086	+	0.445016i	−0.0895580	+	0.995982i	$0.528545\pi$
$264$	5.32181	+	6.67333i	0.327535	+	0.410715i
$265$	−10.4463	+	13.0992i	−0.641709	+	0.804678i
$266$	−13.2291	+	6.37082i	−0.811131	+	0.390620i
$267$	1.83072	+	0.881630i	0.112038	+	0.0539549i
$268$	0.182500	+	0.228848i	0.0111480	+	0.0139791i
$269$	−3.03417	+	13.2935i	−0.184996	+	0.810522i	0.794208	+	0.607646i	$0.207886\pi$
$269$	−3.03417	+	13.2935i	−0.184996	+	0.810522i	−0.979204	+	0.202876i	$0.934971\pi$
$270$	−0.805581	+	3.52948i	−0.0490261	+	0.214797i
$271$	−8.97984	+	11.2604i	−0.545486	+	0.684018i	−0.975801	−	0.218661i	$-0.929831\pi$
$271$	−8.97984	+	11.2604i	−0.545486	+	0.684018i	0.430315	+	0.902679i	$0.358403\pi$
$272$	1.34835	+	5.90751i	0.0817558	+	0.358196i
$273$	−2.01333			−0.121852
$274$	−3.22988	−	14.1510i	−0.195124	−	0.854895i
$275$	11.6761	+	5.62293i	0.704098	+	0.339076i
$276$	−1.63394	−	0.786865i	−0.0983518	−	0.0473637i
$277$	3.05513	+	13.3854i	0.183565	+	0.804251i	0.979915	+	0.199415i	$0.0639041\pi$
$277$	3.05513	+	13.3854i	0.183565	+	0.804251i	−0.796350	+	0.604836i	$0.793239\pi$
$278$	−10.1124			−0.606502
$279$	−0.886819	−	3.88541i	−0.0530924	−	0.232613i
$280$	−10.4268	+	13.0747i	−0.623118	+	0.781365i
$281$	0.0319740	−	0.140087i	0.00190741	−	0.00835691i	−0.973965	−	0.226697i	$-0.927207\pi$
$281$	0.0319740	−	0.140087i	0.00190741	−	0.00835691i	0.975873	+	0.218340i	$0.0700643\pi$
$282$	1.90237	−	8.33482i	0.113284	−	0.496332i
$283$	−5.51039	−	6.90981i	−0.327559	−	0.410746i	0.590596	−	0.806967i	$-0.298893\pi$
$283$	−5.51039	−	6.90981i	−0.327559	−	0.410746i	−0.918155	+	0.396222i	$0.870321\pi$
$284$	6.74701	+	3.24919i	0.400362	+	0.192804i
$285$	−20.2455	+	9.74972i	−1.19924	+	0.577523i
$286$	2.31949	−	2.90855i	0.137155	−	0.171986i
$287$	9.71882	+	12.1870i	0.573684	+	0.719377i
$288$	−3.14352	+	1.51384i	−0.185234	+	0.0892038i
$289$	−10.0164			−0.589199
$290$	−16.2997	−	10.6958i	−0.957149	−	0.628081i
$291$	12.6660			0.742493
$292$	−7.47418	+	3.59937i	−0.437393	+	0.210637i
$293$	−2.10357	−	2.63779i	−0.122892	−	0.154101i	0.716580	−	0.697505i	$-0.245707\pi$
$293$	−2.10357	−	2.63779i	−0.122892	−	0.154101i	−0.839471	+	0.543404i	$0.817135\pi$
$294$	−2.86693	+	3.59501i	−0.167203	+	0.209665i
$295$	22.9808	−	11.0670i	1.33799	−	0.644344i
$296$	29.0432	+	13.9865i	1.68810	+	0.812948i
$297$	−1.72847	−	2.16744i	−0.100296	−	0.125767i
$298$	3.89278	−	17.0554i	0.225503	−	0.987992i
$299$	−0.721003	+	3.15892i	−0.0416967	+	0.182685i
$300$	−1.88087	+	2.35853i	−0.108592	+	0.136170i
$301$	−4.58368	−	20.0824i	−0.264199	−	1.15753i
$302$	17.5561			1.01024
$303$	−0.704365	−	3.08602i	−0.0404647	−	0.177287i
$304$	14.9245	+	7.18728i	0.855981	+	0.412219i
$305$	−13.7553	−	6.62420i	−0.787626	−	0.379301i
$306$	−0.684432	−	2.99869i	−0.0391263	−	0.171424i
$307$	−0.230862			−0.0131760			−0.00658799	−	0.999978i	$-0.502097\pi$
$307$	−0.230862			−0.0131760			−0.00658799	+	0.999978i	$0.502097\pi$
$308$	−0.695152	−	3.04566i	−0.0396100	−	0.173543i
$309$	1.63349	−	2.04833i	0.0929260	−	0.116526i
$310$	−3.21050	+	14.0661i	−0.182344	+	0.798903i
$311$	5.60223	−	24.5450i	0.317673	−	1.39182i	−0.523948	−	0.851750i	$-0.675541\pi$
$311$	5.60223	−	24.5450i	0.317673	−	1.39182i	0.841622	−	0.540068i	$-0.181601\pi$
$312$	2.21329	+	2.77537i	0.125303	+	0.157125i
$313$	−8.99374	−	4.33116i	−0.508356	−	0.244811i	0.162081	−	0.986777i	$-0.448179\pi$
$313$	−8.99374	−	4.33116i	−0.508356	−	0.244811i	−0.670437	+	0.741966i	$0.733894\pi$
$314$	10.4264	−	5.02109i	0.588396	−	0.283357i
$315$	3.38651	−	4.24655i	0.190808	−	0.239266i
$316$	6.20328	+	7.77867i	0.348962	+	0.437584i
$317$	24.9529	−	12.0167i	1.40149	−	0.674924i	0.428030	−	0.903765i	$-0.359208\pi$
$317$	24.9529	−	12.0167i	1.40149	−	0.674924i	0.973464	+	0.228841i	$0.0734935\pi$
$318$	−6.26948			−0.351575
$319$	14.1858	−	4.65190i	0.794251	−	0.260456i
$320$	26.8952			1.50349
$321$	9.04649	−	4.35656i	0.504926	−	0.243160i
$322$	−3.56129	−	4.46571i	−0.198463	−	0.248864i
$323$	11.9033	−	14.9263i	0.662319	−	0.830522i
$324$	0.581409	−	0.279992i	0.0323005	−	0.0155551i
$325$	4.85599	+	2.33852i	0.269362	+	0.129718i
$326$	−1.99160	−	2.49739i	−0.110305	−	0.138318i
$327$	1.02752	−	4.50187i	0.0568221	−	0.248954i
$328$	6.11572	−	26.7947i	0.337684	−	1.47949i
$329$	−7.99720	+	10.0282i	−0.440900	+	0.552871i
$330$	2.23328	+	9.78462i	0.122938	+	0.538626i
$331$	−23.2748			−1.27930			−0.639650	−	0.768666i	$-0.720921\pi$
$331$	−23.2748			−1.27930			−0.639650	+	0.768666i	$0.720921\pi$
$332$	−0.605230	−	2.65169i	−0.0332163	−	0.145530i
$333$	−9.43297	−	4.54268i	−0.516923	−	0.248937i
$334$	3.34465	+	1.61070i	0.183011	+	0.0881335i
$335$	0.313944	+	1.37548i	0.0171526	+	0.0751505i
$336$	−4.00402			−0.218437
$337$	−4.19011	−	18.3581i	−0.228250	−	1.00003i	−0.951066	−	0.308987i	$-0.900010\pi$
$337$	−4.19011	−	18.3581i	−0.228250	−	1.00003i	0.722817	−	0.691040i	$-0.242847\pi$
$338$	−8.46926	+	10.6201i	−0.460667	+	0.577658i
$339$	1.15483	−	5.05965i	0.0627218	−	0.274802i
$340$	1.18033	−	5.17135i	0.0640122	−	0.280456i
$341$	−6.88853	−	8.63794i	−0.373035	−	0.467771i
$342$	−7.57579	−	3.64831i	−0.409652	−	0.197278i
$343$	17.2287	−	8.29692i	0.930264	−	0.447992i
$344$	−22.6446	+	28.3955i	−1.22092	+	1.53098i
$345$	−5.45009	−	6.83419i	−0.293423	−	0.367941i
$346$	−7.94647	+	3.82682i	−0.427205	+	0.205731i
$347$	−19.4007			−1.04148			−0.520741	−	0.853715i	$-0.674344\pi$
$347$	−19.4007			−1.04148			−0.520741	+	0.853715i	$0.674344\pi$
$348$	0.320913	+	3.46028i	0.0172027	+	0.185491i
$349$	9.57141			0.512346			0.256173	−	0.966631i	$-0.417538\pi$
$349$	9.57141			0.512346			0.256173	+	0.966631i	$0.417538\pi$
$350$	−8.56030	+	4.12242i	−0.457567	+	0.220353i
$351$	−0.718855	−	0.901415i	−0.0383696	−	0.0481140i
$352$	−6.03072	+	7.56228i	−0.321438	+	0.403071i
$353$	29.5123	−	14.2124i	1.57078	−	0.756449i	0.572784	−	0.819706i	$-0.305863\pi$
$353$	29.5123	−	14.2124i	1.57078	−	0.756449i	0.997997	+	0.0632575i	$0.0201490\pi$
$354$	8.59933	+	4.14122i	0.457049	+	0.220103i
$355$	22.5050	+	28.2203i	1.19444	+	1.49778i
$356$	−0.291780	+	1.27837i	−0.0154643	+	0.0677536i
$357$	−1.02687	+	4.49900i	−0.0543476	+	0.238113i
$358$	−2.04057	+	2.55880i	−0.107848	+	0.135237i
$359$	−3.23031	−	14.1529i	−0.170489	−	0.746963i	−0.985798	−	0.167936i	$-0.946290\pi$
$359$	−3.23031	−	14.1529i	−0.170489	−	0.746963i	0.815309	−	0.579027i	$-0.196567\pi$
$360$	−9.57670			−0.504736
$361$	−7.38577	−	32.3592i	−0.388725	−	1.70311i
$362$	−7.38320	−	3.55556i	−0.388052	−	0.186876i
$363$	2.98635	+	1.43815i	0.156743	+	0.0754834i
$364$	−0.289107	−	1.26666i	−0.0151533	−	0.0663910i
$365$	−39.9854			−2.09293
$366$	−1.27125	−	5.56971i	−0.0664493	−	0.291133i
$367$	10.7255	−	13.4494i	0.559868	−	0.702052i	−0.418665	−	0.908141i	$-0.637502\pi$
$367$	10.7255	−	13.4494i	0.559868	−	0.702052i	0.978533	+	0.206088i	$0.0660734\pi$
$368$	−1.43390	+	6.28231i	−0.0747470	+	0.327488i
$369$	−1.98633	+	8.70268i	−0.103404	+	0.453043i
$370$	23.6323	+	29.6340i	1.22859	+	1.54060i
$371$	8.47474	+	4.08122i	0.439986	+	0.211886i
$372$	2.31711	−	1.11586i	0.120136	−	0.0578546i
$373$	5.32000	−	6.67107i	0.275459	−	0.345415i	−0.624788	−	0.780795i	$-0.714814\pi$
$373$	5.32000	−	6.67107i	0.275459	−	0.345415i	0.900247	+	0.435380i	$0.143386\pi$
$374$	−5.31645	−	6.66662i	−0.274907	−	0.344722i
$375$	0.911542	−	0.438976i	0.0470718	−	0.0226686i
$376$	22.6152			1.16629
$377$	5.89972	−	1.93468i	0.303851	−	0.0996410i
$378$	2.03246			0.104539
$379$	9.75482	−	4.69767i	0.501071	−	0.241303i	−0.166236	−	0.986086i	$-0.553161\pi$
$379$	9.75482	−	4.69767i	0.501071	−	0.241303i	0.667307	+	0.744783i	$0.267447\pi$
$380$	−9.04107	−	11.3371i	−0.463797	−	0.581583i
$381$	−9.36133	+	11.7387i	−0.479595	+	0.601393i
$382$	−4.64120	+	2.23508i	−0.237464	+	0.114357i
$383$	−18.0481	−	8.69151i	−0.922215	−	0.444115i	−0.0883534	−	0.996089i	$-0.528160\pi$
$383$	−18.0481	−	8.69151i	−0.922215	−	0.444115i	−0.833861	+	0.551974i	$0.813875\pi$
$384$	1.92409	+	2.41274i	0.0981885	+	0.123124i
$385$	3.35064	−	14.6801i	0.170764	−	0.748167i
$386$	1.04610	−	4.58326i	0.0532450	−	0.233282i
$387$	7.35477	−	9.22258i	0.373864	−	0.468810i
$388$	1.81879	+	7.96863i	0.0923349	+	0.404546i
$389$	−30.9606			−1.56976			−0.784881	−	0.619646i	$-0.787276\pi$
$389$	−30.9606			−1.56976			−0.784881	+	0.619646i	$0.787276\pi$
$390$	0.928797	+	4.06933i	0.0470315	+	0.206058i
$391$	6.69121	+	3.22232i	0.338389	+	0.162960i
$392$	−10.9591	−	5.27762i	−0.553518	−	0.266560i
$393$	0.119127	+	0.521929i	0.00600915	+	0.0263278i
$394$	13.9562			0.703103
$395$	10.6711	+	46.7533i	0.536923	+	2.35241i
$396$	1.11541	−	1.39868i	0.0560515	−	0.0702863i
$397$	−4.39793	+	19.2686i	−0.220726	+	0.967063i	0.736208	+	0.676756i	$0.236615\pi$
$397$	−4.39793	+	19.2686i	−0.220726	+	0.967063i	−0.956933	+	0.290307i	$0.906242\pi$
$398$	−0.356643	+	1.56256i	−0.0178769	+	0.0783239i
$399$	7.86561	+	9.86316i	0.393773	+	0.493776i
$400$	9.65735	+	4.65074i	0.482868	+	0.232537i
$401$	−16.7480	+	8.06542i	−0.836356	+	0.402768i	−0.802495	−	0.596659i	$-0.796495\pi$
$401$	−16.7480	+	8.06542i	−0.836356	+	0.402768i	−0.0338611	+	0.999427i	$0.510780\pi$
$402$	−0.329163	+	0.412757i	−0.0164172	+	0.0205865i
$403$	−2.86487	−	3.59243i	−0.142709	−	0.178952i
$404$	1.84038	−	0.886282i	0.0915626	−	0.0440942i
$405$	3.11042			0.154558
$406$	−3.81799	+	10.2576i	−0.189484	+	0.509079i
$407$	−29.0250			−1.43871
$408$	7.33072	−	3.53029i	0.362925	−	0.174775i
$409$	19.6705	+	24.6660i	0.972643	+	1.21966i	0.975576	+	0.219661i	$0.0704950\pi$
$409$	19.6705	+	24.6660i	0.972643	+	1.21966i	−0.00293293	+	0.999996i	$0.500934\pi$
$410$	20.1488	−	25.2657i	0.995076	−	1.24779i
$411$	−11.2359	+	5.41090i	−0.554224	+	0.266900i
$412$	1.52324	+	0.733555i	0.0750448	+	0.0361397i
$413$	−8.92831	−	11.1957i	−0.439333	−	0.550906i
$414$	0.727855	−	3.18894i	0.0357721	−	0.156728i
$415$	2.91721	−	12.7811i	0.143200	−	0.627401i
$416$	−2.50811	+	3.14508i	−0.122970	+	0.154200i
$417$	1.93333	+	8.47048i	0.0946757	+	0.414801i
$418$	−23.3105			−1.14015
$419$	5.20802	+	22.8178i	0.254428	+	1.11472i	0.927110	+	0.374791i	$0.122285\pi$
$419$	5.20802	+	22.8178i	0.254428	+	1.11472i	−0.672681	+	0.739932i	$0.734857\pi$
$420$	3.15795	+	1.52079i	0.154092	+	0.0742069i
$421$	0.355543	+	0.171220i	0.0173281	+	0.00834477i	0.442528	−	0.896755i	$-0.354082\pi$
$421$	0.355543	+	0.171220i	0.0173281	+	0.00834477i	−0.425200	+	0.905100i	$0.639796\pi$
$422$	4.49973	+	19.7146i	0.219044	+	0.959693i
$423$	−7.34522			−0.357137
$424$	−3.69046	−	16.1689i	−0.179224	−	0.785233i
$425$	7.70239	−	9.65850i	0.373621	−	0.468506i
$426$	−3.00552	+	13.1680i	−0.145618	+	0.637994i
$427$	−1.90729	+	8.35636i	−0.0923000	+	0.404393i
$428$	4.03991	+	5.06589i	0.195276	+	0.244869i
$429$	−2.87975	−	1.38681i	−0.139036	−	0.0669560i
$430$	−38.4758	+	18.5290i	−1.85547	+	0.893546i
$431$	−12.9796	+	16.2759i	−0.625205	+	0.783983i	−0.989066	−	0.147470i	$-0.952887\pi$
$431$	−12.9796	+	16.2759i	−0.625205	+	0.783983i	0.363861	+	0.931453i	$0.381458\pi$
$432$	−1.42962	−	1.79269i	−0.0687828	−	0.0862508i
$433$	−0.269212	+	0.129646i	−0.0129375	+	0.00623038i	−0.440341	−	0.897830i	$-0.645143\pi$
$433$	−0.269212	+	0.129646i	−0.0129375	+	0.00623038i	0.427404	+	0.904061i	$0.359428\pi$
$434$	8.10003			0.388814
$435$	−5.84294	+	15.6980i	−0.280147	+	0.752661i
$436$	2.97983			0.142708
$437$	18.2921	−	8.80902i	0.875030	−	0.421392i
$438$	−9.32889	−	11.6981i	−0.445752	−	0.558955i
$439$	16.1485	−	20.2496i	0.770727	−	0.966461i	−0.229249	−	0.973368i	$-0.573627\pi$
$439$	16.1485	−	20.2496i	0.770727	−	0.966461i	0.999976	+	0.00690678i	$0.00219851\pi$
$440$	−23.9199	+	11.5192i	−1.14034	+	0.549156i
$441$	3.55941	+	1.71412i	0.169496	+	0.0816248i
$442$	−2.21106	−	2.77258i	−0.105169	−	0.131878i
$443$	−0.928033	+	4.06598i	−0.0440922	+	0.193181i	−0.992177	−	0.124836i	$-0.960160\pi$
$443$	−0.928033	+	4.06598i	−0.0440922	+	0.193181i	0.948085	+	0.318016i	$0.103017\pi$
$444$	1.50342	−	6.58693i	0.0713494	−	0.312602i
$445$	−3.94059	+	4.94135i	−0.186802	+	0.234242i
$446$	−3.59179	−	15.7367i	−0.170076	−	0.745153i
$447$	−15.0304			−0.710912
$448$	−3.35993	−	14.7208i	−0.158742	−	0.695493i
$449$	19.3037	+	9.29618i	0.910998	+	0.438714i	0.829849	−	0.557988i	$-0.188427\pi$
$449$	19.3037	+	9.29618i	0.910998	+	0.438714i	0.0811496	+	0.996702i	$0.474141\pi$
$450$	−4.90213	−	2.36074i	−0.231089	−	0.111286i
$451$	5.50661	+	24.1260i	0.259296	+	1.13605i
$452$	3.34904			0.157525
$453$	−3.35645	−	14.7056i	−0.157700	−	0.690928i
$454$	1.73477	−	2.17533i	0.0814166	−	0.102093i
$455$	1.39350	−	6.10531i	0.0653281	−	0.286221i
$456$	4.94956	−	21.6854i	0.231784	−	1.01551i
$457$	9.48836	+	11.8980i	0.443847	+	0.556566i	0.952553	−	0.304374i	$-0.0984473\pi$
$457$	9.48836	+	11.8980i	0.443847	+	0.556566i	−0.508706	+	0.860940i	$0.669876\pi$
$458$	−1.12007	−	0.539396i	−0.0523373	−	0.0252043i
$459$	−2.38095	+	1.14660i	−0.111133	+	0.0535189i
$460$	3.51703	−	4.41021i	0.163982	−	0.205627i
$461$	−2.12415	−	2.66360i	−0.0989316	−	0.124056i	0.729901	−	0.683553i	$-0.239566\pi$
$461$	−2.12415	−	2.66360i	−0.0989316	−	0.124056i	−0.828833	+	0.559496i	$0.810995\pi$
$462$	5.07652	−	2.44472i	0.236181	−	0.113739i
$463$	−20.8584			−0.969374			−0.484687	−	0.874688i	$-0.661066\pi$
$463$	−20.8584			−0.969374			−0.484687	+	0.874688i	$0.661066\pi$
$464$	11.7331	−	3.84759i	0.544695	−	0.178620i
$465$	12.3961			0.574853
$466$	26.9170	−	12.9626i	1.24691	−	0.600479i
$467$	10.8132	+	13.5593i	0.500373	+	0.627448i	0.966313	−	0.257368i	$-0.0828553\pi$
$467$	10.8132	+	13.5593i	0.500373	+	0.627448i	−0.465940	+	0.884816i	$0.654284\pi$
$468$	0.463888	−	0.581697i	0.0214432	−	0.0268890i
$469$	0.713635	−	0.343668i	0.0329526	−	0.0158691i
$470$	23.9581	+	11.5376i	1.10511	+	0.532191i
$471$	−6.19919	−	7.77354i	−0.285644	−	0.358186i
$472$	−5.61828	+	24.6153i	−0.258602	+	1.13301i
$473$	7.27685	−	31.8820i	0.334590	−	1.46593i
$474$	−11.1884	+	14.0298i	−0.513901	+	0.644411i
$475$	−7.51495	−	32.9252i	−0.344810	−	1.51071i
$476$	−2.97794			−0.136494
$477$	1.19863	+	5.25152i	0.0548813	+	0.240451i
$478$	8.24191	+	3.96909i	0.376976	+	0.181542i
$479$	32.4935	+	15.6480i	1.48467	+	0.714977i	0.988213	−	0.153087i	$-0.0489214\pi$
$479$	32.4935	+	15.6480i	1.48467	+	0.714977i	0.496452	+	0.868064i	$0.334636\pi$
$480$	−2.41489	−	10.5803i	−0.110224	−	0.482923i
$481$	−12.0712			−0.550399
$482$	−6.33379	−	27.7501i	−0.288496	−	1.26398i
$483$	−3.05976	+	3.83682i	−0.139224	+	0.174581i
$484$	−0.475964	+	2.08534i	−0.0216347	+	0.0947880i
$485$	−8.76656	+	38.4088i	−0.398069	+	1.74405i
$486$	0.725685	+	0.909981i	0.0329178	+	0.0412776i
$487$	−11.8931	−	5.72743i	−0.538929	−	0.259535i	0.144559	−	0.989496i	$-0.453824\pi$
$487$	−11.8931	−	5.72743i	−0.538929	−	0.259535i	−0.683488	+	0.729961i	$0.739538\pi$
$488$	13.6159	−	6.55709i	0.616364	−	0.296825i
$489$	−1.71113	+	2.14569i	−0.0773801	+	0.0970316i
$490$	−8.91736	−	11.1820i	−0.402845	−	0.505152i
$491$	22.3150	−	10.7464i	1.00706	−	0.484976i	0.143734	−	0.989616i	$-0.454089\pi$
$491$	22.3150	−	10.7464i	1.00706	−	0.484976i	0.863330	+	0.504640i	$0.168375\pi$
$492$	−5.76040			−0.259699
$493$	−1.31418	−	14.1703i	−0.0591878	−	0.638199i
$494$	−9.69460			−0.436181
$495$	7.76895	−	3.74133i	0.349188	−	0.168160i
$496$	−5.69751	−	7.14446i	−0.255826	−	0.320796i
$497$	12.6346	−	15.8433i	0.566741	−	0.710671i
$498$	4.41984	−	2.12848i	0.198058	−	0.0953795i
$499$	−14.2485	−	6.86174i	−0.637853	−	0.307174i	0.0868646	−	0.996220i	$-0.472315\pi$
$499$	−14.2485	−	6.86174i	−0.637853	−	0.307174i	−0.724717	+	0.689047i	$0.758030\pi$
$500$	0.407069	+	0.510449i	0.0182047	+	0.0228280i
$501$	0.709729	−	3.10953i	0.0317084	−	0.138923i
$502$	1.54828	−	6.78346i	0.0691031	−	0.302760i
$503$	−14.6226	+	18.3361i	−0.651988	+	0.817568i	−0.992445	−	0.122693i	$-0.960847\pi$
$503$	−14.6226	+	18.3361i	−0.651988	+	0.817568i	0.340456	+	0.940260i	$0.389418\pi$
$504$	1.19639	+	5.24171i	0.0532913	+	0.233484i
$505$	9.84569			0.438127
$506$	−2.01780	−	8.84056i	−0.0897021	−	0.393011i
$507$	10.5149	+	5.06373i	0.466985	+	0.224888i
$508$	−8.72951	−	4.20391i	−0.387309	−	0.186518i
$509$	−1.55265	−	6.80262i	−0.0688202	−	0.301521i	0.928791	−	0.370605i	$-0.120850\pi$
$509$	−1.55265	−	6.80262i	−0.0688202	−	0.301521i	−0.997611	+	0.0690838i	$0.977992\pi$
$510$	9.56706			0.423637
$511$	4.99524	+	21.8856i	0.220976	+	0.968161i
$512$	−13.7914	+	17.2938i	−0.609498	+	0.764286i
$513$	−1.60757	+	7.04323i	−0.0709760	+	0.310966i
$514$	−6.97835	+	30.5741i	−0.307802	+	1.34857i
$515$	5.08084	+	6.37118i	0.223889	+	0.280748i
$516$	6.85838	+	3.30282i	0.301923	+	0.145399i
$517$	−18.3463	+	8.83510i	−0.806868	+	0.388567i
$518$	13.2676	−	16.6370i	0.582943	−	0.730987i
$519$	4.72470	+	5.92459i	0.207391	+	0.260061i
$520$	−9.94804	+	4.79072i	−0.436250	+	0.210087i
$521$	−20.4524			−0.896037			−0.448019	−	0.894024i	$-0.647870\pi$
$521$	−20.4524			−0.896037			−0.448019	+	0.894024i	$0.647870\pi$
$522$	−5.95579	+	1.95306i	−0.260678	+	0.0854832i
$523$	−19.8313			−0.867162			−0.433581	−	0.901115i	$-0.642750\pi$
$523$	−19.8313			−0.867162			−0.433581	+	0.901115i	$0.642750\pi$
$524$	−0.311258	+	0.149894i	−0.0135974	+	0.00654815i
$525$	5.08967	+	6.38224i	0.222131	+	0.278544i
$526$	12.0706	−	15.1361i	0.526303	−	0.659964i
$527$	−9.48885	+	4.56959i	−0.413341	+	0.199055i
$528$	−5.72710	−	2.75803i	−0.249240	−	0.120028i
$529$	−9.41603	−	11.8073i	−0.409393	−	0.513362i
$530$	4.33932	−	19.0118i	0.188488	−	0.825820i
$531$	1.82476	−	7.99481i	0.0791880	−	0.346945i
$532$	−5.07580	+	6.36485i	−0.220064	+	0.275951i
$533$	2.29015	+	10.0338i	0.0991972	+	0.434611i
$534$	−2.36501			−0.102344
$535$	6.94961	+	30.4482i	0.300458	+	1.31639i
$536$	−1.25826	−	0.605944i	−0.0543484	−	0.0261728i
$537$	2.53345	+	1.22005i	0.109327	+	0.0526489i
$538$	−3.53149	−	15.4725i	−0.152253	−	0.667066i
$539$	10.9522			0.471745
$540$	0.446645	+	1.95688i	0.0192205	+	0.0842107i
$541$	22.2616	−	27.9152i	0.957101	−	1.20017i	−0.0226089	−	0.999744i	$-0.507197\pi$
$541$	22.2616	−	27.9152i	0.957101	−	1.20017i	0.979710	−	0.200422i	$-0.0642313\pi$
$542$	3.73017	−	16.3430i	0.160225	−	0.701990i
$543$	−1.56670	+	6.86417i	−0.0672337	+	0.294570i
$544$	5.74878	+	7.20874i	0.246477	+	0.309072i
$545$	12.9404	+	6.23179i	0.554308	+	0.266941i
$546$	2.11127	−	1.01674i	0.0903541	−	0.0435123i
$547$	−6.16194	+	7.72683i	−0.263466	+	0.330376i	−0.895914	−	0.444227i	$-0.853478\pi$
$547$	−6.16194	+	7.72683i	−0.263466	+	0.330376i	0.632449	+	0.774602i	$0.282050\pi$
$548$	−5.01762	−	6.29190i	−0.214342	−	0.268776i
$549$	−4.42233	+	2.12968i	−0.188740	+	0.0908925i
$550$	−15.0837			−0.643172
$551$	−32.5267	−	21.3440i	−1.38568	−	0.909284i
$552$	8.65269			0.368283
$553$	24.2568	−	11.6815i	1.03150	−	0.496746i
$554$	−9.96339	−	12.4937i	−0.423304	−	0.530806i
$555$	20.3043	−	25.4607i	0.861868	−	1.08075i
$556$	−5.05147	+	2.43266i	−0.214230	+	0.103168i
$557$	28.7227	+	13.8321i	1.21702	+	0.586085i	0.928480	−	0.371383i	$-0.121116\pi$
$557$	28.7227	+	13.8321i	1.21702	+	0.586085i	0.288539	+	0.957468i	$0.406830\pi$
$558$	2.89209	+	3.62657i	0.122432	+	0.153525i
$559$	3.02637	−	13.2594i	0.128002	−	0.560813i
$560$	2.77132	−	12.1419i	0.117110	−	0.513090i
$561$	−4.56775	+	5.72778i	−0.192851	+	0.241827i
$562$	0.0372149	+	0.163049i	0.00156981	+	0.00687781i
$563$	−9.06052			−0.381855			−0.190928	−	0.981604i	$-0.561150\pi$
$563$	−9.06052			−0.381855			−0.190928	+	0.981604i	$0.561150\pi$
$564$	−1.05475	−	4.62114i	−0.0444128	−	0.194585i
$565$	14.5438	+	7.00391i	0.611861	+	0.294657i
$566$	9.26791	+	4.46319i	0.389560	+	0.187602i
$567$	−0.388575	−	1.70246i	−0.0163186	−	0.0714965i
$568$	−35.7294			−1.49917
$569$	3.72126	+	16.3039i	0.156003	+	0.683496i	0.991070	+	0.133346i	$0.0425722\pi$
$569$	3.72126	+	16.3039i	0.156003	+	0.683496i	−0.835066	+	0.550150i	$0.814571\pi$
$570$	16.3067	−	20.4480i	0.683014	−	0.856472i
$571$	5.17962	−	22.6934i	0.216761	−	0.949690i	−0.743093	−	0.669188i	$-0.766642\pi$
$571$	5.17962	−	22.6934i	0.216761	−	0.949690i	0.959854	−	0.280502i	$-0.0905009\pi$
$572$	0.458974	−	2.01090i	0.0191907	−	0.0840798i
$573$	2.75950	+	3.46030i	0.115280	+	0.144556i
$574$	−16.3461	−	7.87185i	−0.682272	−	0.328565i
$575$	11.8364	−	5.70013i	0.493613	−	0.237712i
$576$	5.39119	−	6.76034i	0.224633	−	0.281681i
$577$	11.8070	+	14.8056i	0.491533	+	0.616363i	0.964296	−	0.264826i	$-0.0853146\pi$
$577$	11.8070	+	14.8056i	0.491533	+	0.616363i	−0.472763	+	0.881190i	$0.656743\pi$
$578$	10.5036	−	5.05829i	0.436894	−	0.210397i
$579$	−4.03908			−0.167858
$580$	−10.7152	−	1.42183i	−0.444925	−	0.0590383i
$581$	−7.36006			−0.305347
$582$	−13.2821	+	6.39634i	−0.550562	+	0.265137i
$583$	9.31055	+	11.6751i	0.385603	+	0.483531i
$584$	24.6779	−	30.9451i	1.02118	−	1.28052i
$585$	3.23103	−	1.55598i	0.133587	−	0.0643319i
$586$	3.53799	+	1.70381i	0.146153	+	0.0703835i
$587$	−0.0141875	−	0.0177906i	−0.000585581	−	0.000734295i	0.781539	−	0.623857i	$-0.214435\pi$
$587$	−0.0141875	−	0.0177906i	−0.000585581	−	0.000734295i	−0.782124	+	0.623123i	$0.785864\pi$
$588$	−0.567298	+	2.48549i	−0.0233950	+	0.102500i
$589$	−6.40669	+	28.0696i	−0.263983	+	1.15659i
$590$	−18.5099	+	23.2107i	−0.762040	+	0.955568i
$591$	−2.66820	−	11.6902i	−0.109755	−	0.480869i
$592$	−24.0066			−0.986665
$593$	−0.0784633	−	0.343770i	−0.00322210	−	0.0141170i	0.973291	−	0.229574i	$-0.0737332\pi$
$593$	−0.0784633	−	0.343770i	−0.00322210	−	0.0141170i	−0.976513	+	0.215457i	$0.930876\pi$
$594$	2.90711	+	1.39999i	0.119280	+	0.0574424i
$595$	−12.9322	−	6.22783i	−0.530169	−	0.255316i
$596$	−2.15830	−	9.45615i	−0.0884076	−	0.387339i
$597$	1.37703			0.0563582
$598$	−0.839183	−	3.67670i	−0.0343167	−	0.150351i
$599$	5.02946	−	6.30675i	0.205498	−	0.257687i	−0.668393	−	0.743808i	$-0.733017\pi$
$599$	5.02946	−	6.30675i	0.205498	−	0.257687i	0.873891	+	0.486122i	$0.161589\pi$
$600$	3.20275	−	14.0322i	0.130752	−	0.572862i
$601$	4.86790	−	21.3277i	0.198566	−	0.869974i	−0.773226	−	0.634131i	$-0.781358\pi$
$601$	4.86790	−	21.3277i	0.198566	−	0.869974i	0.971791	−	0.235842i	$-0.0757849\pi$
$602$	14.9483	+	18.7446i	0.609247	+	0.763972i
$603$	0.408670	+	0.196805i	0.0166423	+	0.00801451i
$604$	8.76983	−	4.22333i	0.356839	−	0.171845i
$605$	−6.42807	+	8.06054i	−0.261338	+	0.327708i
$606$	2.29707	+	2.88044i	0.0933123	+	0.117010i
$607$	2.92395	−	1.40810i	0.118680	−	0.0571530i	−0.373602	−	0.927589i	$-0.621877\pi$
$607$	2.92395	−	1.40810i	0.118680	−	0.0571530i	0.492281	+	0.870436i	$0.336163\pi$
$608$	25.2061			1.02224
$609$	9.32208	+	1.23697i	0.377750	+	0.0501246i
$610$	17.7697			0.719473
$611$	−7.63003	+	3.67443i	−0.308678	+	0.148651i
$612$	−1.06326	−	1.33329i	−0.0429799	−	0.0538951i
$613$	−5.82061	+	7.29882i	−0.235092	+	0.294797i	−0.885358	−	0.464911i	$-0.846086\pi$
$613$	−5.82061	+	7.29882i	−0.235092	+	0.294797i	0.650265	+	0.759707i	$0.274658\pi$
$614$	0.242092	−	0.116585i	0.00977005	−	0.00470501i
$615$	−25.0155	−	12.0468i	−1.00872	−	0.485776i
$616$	9.29315	+	11.6532i	0.374432	+	0.469522i
$617$	−4.93142	+	21.6059i	−0.198531	+	0.869823i	0.773280	+	0.634064i	$0.218615\pi$
$617$	−4.93142	+	21.6059i	−0.198531	+	0.869823i	−0.971812	+	0.235758i	$0.924243\pi$
$618$	−0.678543	+	2.97289i	−0.0272950	+	0.119587i
$619$	−4.06400	+	5.09610i	−0.163346	+	0.204829i	−0.856768	−	0.515703i	$-0.827531\pi$
$619$	−4.06400	+	5.09610i	−0.163346	+	0.204829i	0.693422	+	0.720532i	$0.256102\pi$
$620$	1.78003	+	7.79880i	0.0714876	+	0.313207i
$621$	−2.81031			−0.112774
$622$	6.52049	+	28.5681i	0.261448	+	1.14548i
$623$	3.19688	+	1.53954i	0.128080	+	0.0616803i
$624$	−2.38185	−	1.14704i	−0.0953501	−	0.0459182i
$625$	5.90138	+	25.8556i	0.236055	+	1.03423i
$626$	11.6185			0.464368
$627$	4.45660	+	19.5256i	0.177979	+	0.779778i
$628$	4.00044	−	5.01639i	0.159635	−	0.200176i
$629$	−6.15672	+	26.9744i	−0.245485	+	1.07554i
$630$	−1.40674	+	6.16332i	−0.0560458	+	0.245553i
$631$	−14.9507	−	18.7476i	−0.595179	−	0.746331i	0.389439	−	0.921052i	$-0.372669\pi$
$631$	−14.9507	−	18.7476i	−0.595179	−	0.746331i	−0.984618	+	0.174721i	$0.944098\pi$
$632$	−42.7687	−	20.5963i	−1.70125	−	0.819278i
$633$	15.6533	−	7.53825i	0.622164	−	0.299618i
$634$	−20.0983	+	25.2025i	−0.798206	+	1.00092i
$635$	−29.1177	−	36.5124i	−1.15550	−	1.44895i
$636$	−3.13180	+	1.50820i	−0.124184	+	0.0598039i
$637$	4.55491			0.180472
$638$	−12.5266	+	12.0420i	−0.495935	+	0.476749i
$639$	11.6046			0.459070
$640$	−8.64820	+	4.16476i	−0.341850	+	0.164626i
$641$	27.4148	+	34.3771i	1.08282	+	1.35781i	0.929154	+	0.369692i	$0.120537\pi$
$641$	27.4148	+	34.3771i	1.08282	+	1.35781i	0.153667	+	0.988123i	$0.450892\pi$
$642$	−7.28650	+	9.13698i	−0.287575	+	0.360608i
$643$	−14.8855	+	7.16846i	−0.587025	+	0.282697i	−0.703727	−	0.710470i	$-0.748482\pi$
$643$	−14.8855	+	7.16846i	−0.587025	+	0.282697i	0.116702	+	0.993167i	$0.462768\pi$
$644$	−2.85325	−	1.37405i	−0.112434	−	0.0541454i
$645$	22.8764	+	28.6861i	0.900758	+	1.12952i
$646$	−4.94458	+	21.6636i	−0.194542	+	0.852343i
$647$	7.84873	−	34.3875i	0.308565	−	1.35191i	−0.548261	−	0.836307i	$-0.684710\pi$
$647$	7.84873	−	34.3875i	0.308565	−	1.35191i	0.856826	−	0.515605i	$-0.172433\pi$
$648$	−1.91967	+	2.40719i	−0.0754116	+	0.0945632i
$649$	−5.05871	−	22.1637i	−0.198572	−	0.870000i
$650$	−6.27317			−0.246054
$651$	−1.54860	−	6.78485i	−0.0606943	−	0.265919i
$652$	−1.59564	−	0.768422i	−0.0624903	−	0.0300937i
$653$	−15.1503	−	7.29602i	−0.592878	−	0.285515i	0.113287	−	0.993562i	$-0.463862\pi$
$653$	−15.1503	−	7.29602i	−0.592878	−	0.285515i	−0.706165	+	0.708047i	$0.749576\pi$
$654$	1.19594	+	5.23976i	0.0467650	+	0.204891i
$655$	−1.66517			−0.0650635
$656$	4.55453	+	19.9547i	0.177824	+	0.779100i
$657$	−8.01514	+	10.0507i	−0.312700	+	0.392114i
$658$	3.32199	−	14.5546i	0.129505	−	0.567397i
$659$	−0.668451	+	2.92867i	−0.0260392	+	0.114085i	−0.986277	−	0.165097i	$-0.947206\pi$
$659$	−0.668451	+	2.92867i	−0.0260392	+	0.114085i	0.960238	+	0.279182i	$0.0900633\pi$
$660$	3.46940	+	4.35049i	0.135046	+	0.169342i
$661$	−34.5193	−	16.6236i	−1.34264	−	0.646583i	−0.381948	−	0.924184i	$-0.624746\pi$
$661$	−34.5193	−	16.6236i	−1.34264	−	0.646583i	−0.960697	+	0.277601i	$0.910461\pi$
$662$	24.4071	−	11.7538i	0.948607	−	0.456825i
$663$	−1.89968	+	2.38213i	−0.0737776	+	0.0925141i
$664$	8.09102	+	10.1458i	0.313992	+	0.393734i
$665$	−35.3535	+	17.0253i	−1.37095	+	0.660214i
$666$	12.1859			0.472194
$667$	5.27918	−	14.1834i	0.204411	−	0.549183i
$668$	2.05823			0.0796353
$669$	−12.4949	+	6.01721i	−0.483079	+	0.232639i
$670$	−1.02384	−	1.28385i	−0.0395542	−	0.0495994i
$671$	−8.48405	+	10.6387i	−0.327523	+	0.410701i
$672$	−5.48934	+	2.64353i	−0.211756	+	0.101976i
$673$	24.6701	+	11.8805i	0.950963	+	0.457960i	0.844024	−	0.536306i	$-0.180181\pi$
$673$	24.6701	+	11.8805i	0.950963	+	0.457960i	0.106939	+	0.994266i	$0.465895\pi$
$674$	13.6648	+	17.1351i	0.526348	+	0.660019i
$675$	−1.04022	+	4.55752i	−0.0400383	+	0.175419i
$676$	−1.67587	+	7.34246i	−0.0644565	+	0.282402i
$677$	17.8546	−	22.3890i	0.686209	−	0.860479i	−0.309700	−	0.950834i	$-0.600229\pi$
$677$	17.8546	−	22.3890i	0.686209	−	0.860479i	0.995910	+	0.0903549i	$0.0288001\pi$
$678$	1.34412	+	5.88897i	0.0516206	+	0.226165i
$679$	22.1178			0.848805
$680$	5.63154	+	24.6734i	0.215960	+	0.946181i
$681$	−2.15378	−	1.03721i	−0.0825332	−	0.0397459i
$682$	11.5858	+	5.57943i	0.443643	+	0.213647i
$683$	−2.80121	−	12.2729i	−0.107185	−	0.469609i	−0.999823	−	0.0188337i	$-0.994005\pi$
$683$	−2.80121	−	12.2729i	−0.107185	−	0.469609i	0.892637	−	0.450775i	$-0.148852\pi$
$684$	−4.66199			−0.178256
$685$	−8.63150	−	37.8171i	−0.329793	−	1.44492i
$686$	−13.8769	+	17.4011i	−0.529822	+	0.664376i
$687$	−0.237676	+	1.04133i	−0.00906792	+	0.0397292i
$688$	6.01870	−	26.3696i	0.229461	−	1.00533i
$689$	3.87216	+	4.85554i	0.147518	+	0.184981i
$690$	9.16649	+	4.41435i	0.348962	+	0.168051i
$691$	−36.0563	+	17.3638i	−1.37165	+	0.660550i	−0.967201	−	0.254012i	$-0.918250\pi$
$691$	−36.0563	+	17.3638i	−1.37165	+	0.660550i	−0.404446	+	0.914562i	$0.632536\pi$
$692$	−3.04892	+	3.82323i	−0.115903	+	0.145337i
$693$	−3.01833	−	3.78486i	−0.114657	−	0.143775i
$694$	20.3444	−	9.79736i	0.772264	−	0.371903i
$695$	−27.0243			−1.02509
$696$	−8.54274	−	14.2103i	−0.323812	−	0.538639i
$697$	23.5896			0.893520
$698$	−10.0370	+	4.83358i	−0.379907	+	0.182954i
$699$	−16.0040	−	20.0683i	−0.605326	−	0.759054i
$700$	−3.28444	+	4.11856i	−0.124140	+	0.155667i
$701$	11.6102	−	5.59119i	0.438512	−	0.211176i	−0.201584	−	0.979471i	$-0.564609\pi$
$701$	11.6102	−	5.59119i	0.438512	−	0.211176i	0.640096	+	0.768295i	$0.278895\pi$
$702$	1.20904	+	0.582243i	0.0456323	+	0.0219753i
$703$	47.1593	+	59.1359i	1.77865	+	2.23035i
$704$	5.33408	−	23.3701i	0.201036	−	0.880795i
$705$	5.08388	−	22.2739i	0.191470	−	0.838884i
$706$	−23.7707	+	29.8075i	−0.894622	+	1.12182i
$707$	−1.22999	−	5.38894i	−0.0462585	−	0.202672i
$708$	5.29186			0.198880
$709$	0.139525	+	0.611300i	0.00523998	+	0.0229578i	0.977480	−	0.211027i	$-0.0676807\pi$
$709$	0.139525	+	0.611300i	0.00523998	+	0.0229578i	−0.972240	+	0.233984i	$0.924824\pi$
$710$	−37.8511	−	18.2281i	−1.42052	−	0.684089i
$711$	13.8909	+	6.68950i	0.520949	+	0.250876i
$712$	−1.39213	−	6.09933i	−0.0521724	−	0.228582i
$713$	−11.2000			−0.419444
$714$	−1.19518	−	5.23643i	−0.0447285	−	0.195969i
$715$	6.19860	−	7.77280i	0.231814	−	0.290686i
$716$	−0.403781	+	1.76908i	−0.0150900	+	0.0661137i
$717$	1.74892	−	7.66252i	0.0653146	−	0.286162i
$718$	10.5347	+	13.2101i	0.393151	+	0.492996i
$719$	−31.9194	−	15.3716i	−1.19039	−	0.573263i	−0.269471	−	0.963009i	$-0.586849\pi$
$719$	−31.9194	−	15.3716i	−1.19039	−	0.573263i	−0.920923	+	0.389745i	$0.872563\pi$
$720$	6.42571	−	3.09446i	0.239472	−	0.115324i
$721$	2.85247	−	3.57688i	0.106231	−	0.133210i
$722$	24.0865	+	30.2035i	0.896406	+	1.12406i
$723$	−22.0335	+	10.6108i	−0.819435	+	0.394619i
$724$	−4.54347			−0.168857
$725$	−21.0473	−	13.8112i	−0.781677	−	0.512936i
$726$	−3.85790			−0.143180
$727$	17.5000	−	8.42754i	0.649038	−	0.312560i	−0.0802424	−	0.996775i	$-0.525569\pi$
$727$	17.5000	−	8.42754i	0.649038	−	0.312560i	0.729280	+	0.684215i	$0.239855\pi$
$728$	3.86493	+	4.84647i	0.143244	+	0.179622i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	41.9305	−	20.1927i	1.55192	−	0.747364i
$731$	−28.0860	−	13.5255i	−1.03880	−	0.500258i
$732$	−1.97489	−	2.47643i	−0.0729940	−	0.0915315i
$733$	5.58097	−	24.4518i	0.206138	−	0.903148i	−0.760971	−	0.648786i	$-0.775277\pi$
$733$	5.58097	−	24.4518i	0.206138	−	0.903148i	0.967109	−	0.254363i	$-0.0818656\pi$
$734$	−4.45532	+	19.5201i	−0.164449	+	0.720498i
$735$	−7.66156	+	9.60729i	−0.282601	+	0.354370i
$736$	2.18189	+	9.55947i	0.0804254	+	0.352367i
$737$	1.25746			0.0463193
$738$	−2.31191	−	10.1291i	−0.0851025	−	0.372858i
$739$	−47.6184	−	22.9318i	−1.75167	−	0.843560i	−0.977603	−	0.210458i	$-0.932505\pi$
$739$	−47.6184	−	22.9318i	−1.75167	−	0.843560i	−0.774068	−	0.633103i	$-0.781781\pi$
$740$	18.9339	+	9.11808i	0.696024	+	0.335187i
$741$	1.85345	+	8.12051i	0.0680883	+	0.298314i
$742$	−10.9480			−0.401914
$743$	−3.53331	−	15.4804i	−0.129625	−	0.567922i	−0.997470	−	0.0710881i	$-0.977353\pi$
$743$	−3.53331	−	15.4804i	−0.129625	−	0.567922i	0.867845	−	0.496834i	$-0.165504\pi$
$744$	−7.65050	+	9.59342i	−0.280481	+	0.351712i
$745$	10.4030	−	45.5787i	0.381138	−	1.66987i
$746$	−2.20990	+	9.68219i	−0.0809101	+	0.354490i
$747$	−2.62789	−	3.29527i	−0.0961494	−	0.120567i
$748$	−4.25947	−	2.05125i	−0.155741	−	0.0750011i
$749$	15.7973	−	7.60760i	0.577222	−	0.277976i
$750$	−0.734202	+	0.920660i	−0.0268093	+	0.0336177i
$751$	−5.78372	−	7.25256i	−0.211051	−	0.264650i	0.665027	−	0.746820i	$-0.268420\pi$
$751$	−5.78372	−	7.25256i	−0.211051	−	0.264650i	−0.876078	+	0.482170i	$0.839849\pi$
$752$	−15.1742	+	7.30752i	−0.553347	+	0.266478i
$753$	−5.97805			−0.217852
$754$	−5.20971	+	5.00816i	−0.189726	+	0.182386i
$755$	46.9168			1.70748
$756$	1.01528	−	0.488933i	0.0369254	−	0.0177823i
$757$	−3.73161	−	4.67930i	−0.135628	−	0.170072i	0.709379	−	0.704827i	$-0.248975\pi$
$757$	−3.73161	−	4.67930i	−0.135628	−	0.170072i	−0.845007	+	0.534755i	$0.820404\pi$
$758$	−7.85702	+	9.85239i	−0.285380	+	0.357855i
$759$	−7.01936	+	3.38035i	−0.254787	+	0.122699i
$760$	62.3340	+	30.0185i	2.26109	+	1.08888i
$761$	13.1939	+	16.5446i	0.478279	+	0.599743i	0.961177	−	0.275934i	$-0.0889872\pi$
$761$	13.1939	+	16.5446i	0.478279	+	0.599743i	−0.482898	+	0.875677i	$0.660416\pi$
$762$	3.88864	−	17.0373i	0.140871	−	0.617195i
$763$	1.79430	−	7.86134i	0.0649580	−	0.284599i
$764$	−1.78075	+	2.23299i	−0.0644252	+	0.0807866i
$765$	−1.82907	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04865 + 0.505001i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.402348 + 0.504528i) q^{4} +(-2.80239 + 1.34956i) q^{5} +(-1.04865 - 0.505001i) q^{6} +(1.08876 + 1.36527i) q^{7} +(0.685121 - 3.00171i) q^{8} +(-0.222521 + 0.974928i) q^{9} +O(q^{10})\)	\(q+(-1.04865 + 0.505001i) q^{2} +(0.623490 + 0.781831i) q^{3} +(-0.402348 + 0.504528i) q^{4} +(-2.80239 + 1.34956i) q^{5} +(-1.04865 - 0.505001i) q^{6} +(1.08876 + 1.36527i) q^{7} +(0.685121 - 3.00171i) q^{8} +(-0.222521 + 0.974928i) q^{9} +(2.25719 - 2.83042i) q^{10} +(0.616885 + 2.70275i) q^{11} -0.645316 q^{12} +(0.256556 + 1.12405i) q^{13} +(-1.83119 - 0.881853i) q^{14} +(-2.80239 - 1.34956i) q^{15} +(0.510226 + 2.23545i) q^{16} +2.64265 q^{17} +(-0.258994 - 1.13473i) q^{18} +(4.50431 - 5.64823i) q^{19} +(0.446645 - 1.95688i) q^{20} +(-0.388575 + 1.70246i) q^{21} +(-2.01179 - 2.52270i) q^{22} +(2.53201 + 1.21935i) q^{23} +(2.77400 - 1.33589i) q^{24} +(2.91464 - 3.65485i) q^{25} +(-0.836681 - 1.04917i) q^{26} +(-0.900969 + 0.433884i) q^{27} -1.12688 q^{28} +(-0.497296 - 5.36215i) q^{29} +3.62025 q^{30} +(-3.59066 + 1.72917i) q^{31} +(2.17538 + 2.72784i) q^{32} +(-1.72847 + 2.16744i) q^{33} +(-2.77121 + 1.33454i) q^{34} +(-4.89365 - 2.35666i) q^{35} +(-0.402348 - 0.504528i) q^{36} +(-2.32975 + 10.2073i) q^{37} +(-1.87107 + 8.19768i) q^{38} +(-0.718855 + 0.901415i) q^{39} +(2.13102 + 9.33659i) q^{40} +8.92649 q^{41} +(-0.452266 - 1.98151i) q^{42} +(-10.6279 - 5.11815i) q^{43} +(-1.61181 - 0.776209i) q^{44} +(-0.692134 - 3.03244i) q^{45} -3.27095 q^{46} +(1.63447 + 7.16106i) q^{47} +(-1.42962 + 1.79269i) q^{48} +(0.879102 - 3.85160i) q^{49} +(-1.21073 + 5.30454i) q^{50} +(1.64767 + 2.06611i) q^{51} +(-0.670338 - 0.322818i) q^{52} +(4.85314 - 2.33715i) q^{53} +(0.725685 - 0.909981i) q^{54} +(-5.37628 - 6.74164i) q^{55} +(4.84407 - 2.33278i) q^{56} +7.22436 q^{57} +(3.22938 + 5.37187i) q^{58} -8.20042 q^{59} +(1.80843 - 0.870893i) q^{60} +(3.06034 + 3.83755i) q^{61} +(2.89209 - 3.62657i) q^{62} +(-1.57331 + 0.757665i) q^{63} +(-7.79050 - 3.75171i) q^{64} +(-2.23594 - 2.80378i) q^{65} +(0.717998 - 3.14575i) q^{66} +(0.100933 - 0.442217i) q^{67} +(-1.06326 + 1.33329i) q^{68} +(0.625354 + 2.73985i) q^{69} +6.32182 q^{70} +(-2.58226 - 11.3136i) q^{71} +(2.77400 + 1.33589i) q^{72} +(11.5822 + 5.57770i) q^{73} +(-2.71162 - 11.8804i) q^{74} +4.67473 q^{75} +(1.03739 + 4.54510i) q^{76} +(-3.01833 + 3.78486i) q^{77} +(0.298608 - 1.30829i) q^{78} +(3.43076 - 15.0312i) q^{79} +(-4.44673 - 5.57602i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(-9.36072 + 4.50789i) q^{82} +(-2.62789 + 3.29527i) q^{83} +(-0.702595 - 0.881027i) q^{84} +(-7.40575 + 3.56642i) q^{85} +13.7296 q^{86} +(3.88224 - 3.73205i) q^{87} +8.53551 q^{88} +(1.83072 - 0.881630i) q^{89} +(2.25719 + 2.83042i) q^{90} +(-1.25529 + 1.57409i) q^{91} +(-1.63394 + 0.786865i) q^{92} +(-3.59066 - 1.72917i) q^{93} +(-5.33032 - 6.68401i) q^{94} +(-5.00022 + 21.9074i) q^{95} +(-0.776385 + 3.40157i) q^{96} +(7.89711 - 9.90266i) q^{97} +(1.02319 + 4.48291i) q^{98} -2.77225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Introduction

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